School of IoT Engineering, Jiangnan University, Wuxi 214122, Jiangsu Province, China.
Comput Biol Med. 2011 Apr;41(4):221-7. doi: 10.1016/j.compbiomed.2011.02.003.
In order to predict variations of drug concentration during a given period of time, numerical solutions of pharmacokinetic models need to be obtained efficiently. Analytical solutions of linear pharmacokinetic models are usually obtained using the Laplace transform and inverse Laplace tables. The derivations of solutions to complex nonlinear models are tedious, and such solution process may be difficult to implement as a robust software code. For nonlinear models, the fourth-order Runge-Kutta (RK4) is the most classical numerical method in obtaining approximate numerical solutions, which is impossible to be implemented in distributed computing environments without much modification. The reason is that numerical solutions obtained by using RK4 can only be computed in sequential time steps. In this paper, time-domain decomposition methods are adapted for nonlinear pharmacokinetic models. The numerical Inverse Laplace method for PharmacoKinetic models (ILPK) is implemented to solve pharmacokinetic models with iterative inverse Laplace transform in each time interval. The distributed ILPK algorithm, which is based on a two-level time-domain decomposition concept, is proposed to improve its efficiency. Solutions on the coarser temporal mesh at the top level are obtained one by one, and then those on the finer temporal mesh at the bottom level are calculated concurrently by using those initial solutions that have been obtained at the top level decomposition. Accuracy and efficiency of the proposed algorithm and its distributed equivalent are investigated by using several test models. Results indicate that the ILPK algorithm and its distributed equivalent are good candidates for both linear and nonlinear pharmacokinetic models.
为了预测给定时间段内药物浓度的变化，需要有效地获得药代动力学模型的数值解。线性药代动力学模型的解析解通常使用拉普拉斯变换和逆拉普拉斯表获得。复杂非线性模型解的推导很繁琐，并且这种解决方案可能难以作为稳健的软件代码实现。对于非线性模型，四阶龙格-库塔（RK4）是获得近似数值解的最经典数值方法，如果不进行大量修改，则无法在分布式计算环境中实现。原因是使用 RK4 获得的数值解只能在顺序时间步长中进行计算。在本文中，适用于非线性药代动力学模型的时域分解方法。实现了用于药代动力学模型的时域逆拉普拉斯方法（ILPK），该方法在每个时间间隔中使用迭代逆拉普拉斯变换来求解药代动力学模型。基于两级时域分解概念的分布式 ILPK 算法被提出以提高其效率。在顶层较粗的时间网格上获得一个解决方案，然后通过使用在顶层分解中已经获得的那些初始解决方案同时计算底层较细的时间网格上的解决方案。通过使用几个测试模型研究了所提出算法及其分布式等效算法的准确性和效率。结果表明，ILPK 算法及其分布式等效算法是线性和非线性药代动力学模型的很好选择。
